Mathematical problems of the theory of open quantum systems and the geometry of space-time

The project, supported by the Russian Science Foundation, is devoted to the study of mathematical problems of the theory of quantum open systems, taking into account the geometric properties of space-time.
The project will explore the connections between the theory of open quantum systems and the theory of general relativity. One example of open systems is quantum systems on nontrivial Lorentzian manifolds (gravitational fields) in the presence of black holes. In particular, one of the important problems of modern mathematical physics will be studied — the problem of information loss in black holes during Hawking radiation. The study of these issues is closely related to the fundamental problems of irreversibility of time, thermalization and entropy increase in statistical mechanics.
An actual task is also the task of modeling Hawking radiation using quantum dynamical systems. The entropy of the simplest eternal black hole is modeled using an analytical continuation of the Bose entropy of a gas, which allows representation in the form of the Riemann zeta function. Of indisputable interest is the generalization of this representation to the case of more complex black holes, which is also one of the goals of the project.